Finite Group Databasebeta

C3×C2503 #21418911

order7509
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C9×C139 (order 5004) · Inn(G) = C1 · Out(G) = C22×C9×C139
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7509
abelianC3×C2503

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

4 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7509 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD7509, Dic7509, D3×D2503, …
Fitting subgroup ofD3×C2503, C3×D2503, D7509, …
socle ofD3×C2503, C3×D2503, D7509, …
maximal subgroup ofD3×C2503, C3×D2503, D7509, …
maximal normal subgroup ofD3×C2503, C3×D2503, D7509, …
maximal quotient ofC2×C3×C2503, C9×C2503, C32×C2503, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7509, 2);